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∫03∫0sqrt(9-x2)∫sqrt(x2+y2)sqrt(18-x2-y2) (x2+y2+z2)dzdxdy
x=\rhosin\varphicosθ
y=\rhosin\varphisinθ
z=\rhocos\varphi
Change the integrand to \rho and integrate wrt d\rhodθd\varphi
I don't know how to find the limits of integration. Normally I would draw a picture and reason it out, but that doesn't seem plausible here.
Thanks.
x=\rhosin\varphicosθ
y=\rhosin\varphisinθ
z=\rhocos\varphi
Change the integrand to \rho and integrate wrt d\rhodθd\varphi
I don't know how to find the limits of integration. Normally I would draw a picture and reason it out, but that doesn't seem plausible here.
Thanks.